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satellite image processing satellite image processing Document Transcript

  • DIGITAL IMAGE PROCESSINGMinakshi KumarPhotogrammetry and Remote Sensing DivisionIndian Institute of Remote Sensing, Dehra Dun Abstract : This paper describes the basic technological aspects of Digital Image Processing with special reference to satellite image processing. Basically, all satellite image-processing operations can be grouped into three categories: Image Rectification and Restoration, Enhancement and Information Extraction. The former deals with initial processing of raw image data to correct for geometric distortion, to calibrate the data radiometrically and to eliminate noise present in the data. The enhancement procedures are applied to image data in order to effectively display the data for subsequent visual interpretation. It involves techniques for increasing the visual distinction between features in a scene. The objective of the information extraction operations is to replace visual analysis of the image data with quantitative techniques for automating the identification of features in a scene. This involves the analysis of multispectral image data and the application of statistically based decision rules for determining the land cover identity of each pixel in an image. The intent of classification process is to categorize all pixels in a digital image into one of several land cover classes or themes. This classified data may be used to produce thematic maps of the land cover present in an image.INTRODUCTION Pictures are the most common and convenient means of conveying ortransmitting information. A picture is worth a thousand words. Picturesconcisely convey information about positions, sizes and inter-relationshipsbetween objects. They portray spatial information that we can recognize asobjects. Human beings are good at deriving information from such images,because of our innate visual and mental abilities. About 75% of theinformation received by human is in pictorial form. In the present context, the analysis of pictures that employ an overheadperspective, including the radiation not visible to human eye are considered.Satellite Remote Sensing and GIS Applications in Agricultural Meteorologypp. 81-102
  • 82 Digital Image ProcessingThus our discussion will be focussing on analysis of remotely sensed images.These images are represented in digital form. When represented as numbers,brightness can be added, subtracted, multiplied, divided and, in general,subjected to statistical manipulations that are not possible if an image ispresented only as a photograph. Although digital analysis of remotely senseddata dates from the early days of remote sensing, the launch of the first Landsatearth observation satellite in 1972 began an era of increasing interest inmachine processing (Cambell, 1996 and Jensen, 1996). Previously, digitalremote sensing data could be analyzed only at specialized remote sensinglaboratories. Specialized equipment and trained personnel necessary to conductroutine machine analysis of data were not widely available, in part because oflimited availability of digital remote sensing data and a lack of appreciationof their qualities.DIGITAL IMAGE A digital remotely sensed image is typically composed of picture elements(pixels) located at the intersection of each row i and column j in each K bandsof imagery. Associated with each pixel is a number known as Digital Number(DN) or Brightness Value (BV), that depicts the average radiance of a relativelysmall area within a scene (Fig. 1). A smaller number indicates low averageradiance from the area and the high number is an indicator of high radiantproperties of the area. The size of this area effects the reproduction of details within the scene.As pixel size is reduced more scene detail is presented in digital representation. Origin (0,0) Scan Pixels Scan Lines Lines 110 15 17 20 21 2 3 Bands15 16 18 21 23 417 18 20 22 2418 20 22 24 2618 20 22 25 25 Pixels Figure 1 : Structure of a Digital Image and Multispectral Image
  • Minakshi Kumar 83COLOR COMPOSITES While displaying the different bands of a multispectral data set, imagesobtained in different bands are displayed in image planes (other than theirown) the color composite is regarded as False Color Composite (FCC). Highspectral resolution is important when producing color components. For a truecolor composite an image data used in red, green and blue spectral regionmust be assigned bits of red, green and blue image processor frame buffermemory. A color infrared composite ‘standard false color composite’ isdisplayed by placing the infrared, red, green in the red, green and blue framebuffer memory (Fig. 2). In this healthy vegetation shows up in shades of redbecause vegetation absorbs most of green and red energy but reflectsapproximately half of incident Infrared energy. Urban areas reflect equalportions of NIR, R & G, and therefore they appear as steel grey. Screen Colour Gun Assignment Green Blue Gun Red Green Gun Infrared Red Gun Figure 2: False Color Composite (FCC) of IRS : LISS II Poanta areaIMAGE RECTIFICATION AND REGISTRATION Geometric distortions manifest themselves as errors in the position of apixel relative to other pixels in the scene and with respect to their absoluteposition within some defined map projection. If left uncorrected, thesegeometric distortions render any data extracted from the image useless. Thisis particularly so if the information is to be compared to other data sets, be itfrom another image or a GIS data set. Distortions occur for many reasons. View slide
  • 84 Digital Image ProcessingFor instance distortions occur due to changes in platform attitude (roll, pitchand yaw), altitude, earth rotation, earth curvature, panoramic distortion anddetector delay. Most of these distortions can be modelled mathematically andare removed before you buy an image. Changes in attitude however can bedifficult to account for mathematically and so a procedure called imagerectification is performed. Satellite systems are however geometrically quitestable and geometric rectification is a simple procedure based on a mappingtransformation relating real ground coordinates, say in easting and northing,to image line and pixel coordinates.Rectification is a process of geometrically correcting an image so that it canbe represented on a planar surface , conform to other images or conform to amap (Fig. 3). That is, it is the process by which geometry of an image is madeplanimetric. It is necessary when accurate area, distance and directionmeasurements are required to be made from the imagery. It is achieved bytransforming the data from one grid system into another grid system using ageometric transformation. Rectification is not necessary if there is no distortion in the image. Forexample, if an image file is produced by scanning or digitizing a paper mapthat is in the desired projection system, then that image is already planar anddoes not require rectification unless there is some skew or rotation of the image.Scanning and digitizing produce images that are planar, but do not containany map coordinate information. These images need only to be geo-referenced,which is a much simpler process than rectification. In many cases, the imageheader can simply be updated with new map coordinate information. Thisinvolves redefining the map coordinate of the upper left corner of the imageand the cell size (the area represented by each pixel). Ground Control Points (GCP) are the specific pixels in the input imagefor which the output map coordinates are known. By using more points thannecessary to solve the transformation equations a least squares solution maybe found that minimises the sum of the squares of the errors. Care should beexercised when selecting ground control points as their number, quality anddistribution affect the result of the rectification. Once the mapping transformation has been determined a procedure calledresampling is employed. Resampling matches the coordinates of image pixelsto their real world coordinates and writes a new image on a pixel by pixelbasis. Since the grid of pixels in the source image rarely matches the grid for View slide
  • Minakshi Kumar 85 (A) (B) (C) (D)Figure 3 : Image Rectification (a & b) Input and reference image with GCP locations, (c) usingpolynomial equations the grids are fitted together, (d) using resampling method the output gridpixel values are assigned (source modified from ERDAS Field guide)the reference image, the pixels are resampled so that new data file values forthe output file can be calculated.IMAGE ENHANCEMENT TECHNIQUES Image enhancement techniques improve the quality of an image asperceived by a human. These techniques are most useful because many satelliteimages when examined on a colour display give inadequate information forimage interpretation. There is no conscious effort to improve the fidelity ofthe image with regard to some ideal form of the image. There exists a widevariety of techniques for improving image quality. The contrast stretch, densityslicing, edge enhancement, and spatial filtering are the more commonly usedtechniques. Image enhancement is attempted after the image is corrected forgeometric and radiometric distortions. Image enhancement methods areapplied separately to each band of a multispectral image. Digital techniques
  • 86 Digital Image Processinghave been found to be most satisfactory than the photographic technique forimage enhancement, because of the precision and wide variety of digitalprocesses.Contrast Contrast generally refers to the difference in luminance or grey level valuesin an image and is an important characteristic. It can be defined as the ratioof the maximum intensity to the minimum intensity over an image. Contrast ratio has a strong bearing on the resolving power and detectabilityof an image. Larger this ratio, more easy it is to interpret the image. Satelliteimages lack adequate contrast and require contrast improvement.Contrast Enhancement Contrast enhancement techniques expand the range of brightness valuesin an image so that the image can be efficiently displayed in a manner desiredby the analyst. The density values in a scene are literally pulled farther apart,that is, expanded over a greater range. The effect is to increase the visualcontrast between two areas of different uniform densities. This enables theanalyst to discriminate easily between areas initially having a small differencein density.Linear Contrast Stretch This is the simplest contrast stretch algorithm. The grey values in theoriginal image and the modified image follow a linear relation in thisalgorithm. A density number in the low range of the original histogram isassigned to extremely black and a value at the high end is assigned to extremelywhite. The remaining pixel values are distributed linearly between theseextremes. The features or details that were obscure on the original image willbe clear in the contrast stretched image. Linear contrast stretch operation canbe represented graphically as shown in Fig. 4. To provide optimal contrastand colour variation in colour composites the small range of grey values ineach band is stretched to the full brightness range of the output or displayunit.
  • Minakshi Kumar 87 Histogram of Transformation Histogram of min-max low contrast image linear contrast255 255 stretched iamge h etc str ast Frequency Frequency ntr BV out o rc ea maxk lin min k maxk min k 0 4 Bandk 104 255 4 BV in 104 0 0 255 0 BV out 255 BV in (a)(a) Histogram Image values (DN)(b) No stretch Display levels (DN) Image values (DN)(c) Linear stretch Display levels (DN) Figure 4: Linear Contrast Stretch (source Lillesand and Kiefer, 1993)Non-Linear Contrast Enhancement In these methods, the input and output data values follow a non-lineartransformation. The general form of the non-linear contrast enhancement isdefined by y = f (x), where x is the input data value and y is the output datavalue. The non-linear contrast enhancement techniques have been found tobe useful for enhancing the colour contrast between the nearly classes andsubclasses of a main class. A type of non linear contrast stretch involves scaling the input datalogarithmically. This enhancement has greatest impact on the brightness valuesfound in the darker part of histogram. It could be reversed to enhance valuesin brighter part of histogram by scaling the input data using an inverse logfunction.
  • 88 Digital Image Processing Histogram equalization is another non-linear contrast enhancementtechnique. In this technique, histogram of the original image is redistributedto produce a uniform population density. This is obtained by grouping certainadjacent grey values. Thus the number of grey levels in the enhanced imageis less than the number of grey levels in the original image.SPATIAL FILTERING A characteristic of remotely sensed images is a parameter called spatialfrequency defined as number of changes in Brightness Value per unit distancefor any particular part of an image. If there are very few changes in BrightnessValue once a given area in an image, this is referred to as low frequency area.Conversely, if the Brightness Value changes dramatically over short distances,this is an area of high frequency. Spatial filtering is the process of dividing the image into its constituentspatial frequencies, and selectively altering certain spatial frequencies toemphasize some image features. This technique increases the analyst’s abilityto discriminate detail. The three types of spatial filters used in remote sensordata processing are : Low pass filters, Band pass filters and High pass filters.Low-Frequency Filtering in the Spatial Domain Image enhancements that de-emphasize or block the high spatial frequencydetail are low-frequency or low-pass filters. The simplest low-frequency filterevaluates a particular input pixel brightness value, BV in, and the pixelssurrounding the input pixel, and outputs a new brightness value, BVout , thatis the mean of this convolution. The size of the neighbourhood convolutionmask or kernel (n) is usually 3x3, 5x5, 7x7, or 9x9. The simple smoothing operation will, however, blur the image, especiallyat the edges of objects. Blurring becomes more severe as the size of the kernelincreases. Using a 3x3 kernel can result in the low-pass image being two lines andtwo columns smaller than the original image. Techniques that can be appliedto deal with this problem include (1) artificially extending the original imagebeyond its border by repeating the original border pixel brightness values or(2) replicating the averaged brightness values near the borders, based on the
  • Minakshi Kumar 89image behaviour within a view pixels of the border. The most commonly usedlow pass filters are mean, median and mode filters.High-Frequency Filtering in the Spatial Domain High-pass filtering is applied to imagery to remove the slowly varyingcomponents and enhance the high-frequency local variations. Brightness valuestend to be highly correlated in a nine-element window. Thus, the high-frequency filtered image will have a relatively narrow intensity histogram. Thissuggests that the output from most high-frequency filtered images must becontrast stretched prior to visual analysis.Edge Enhancement in the Spatial Domain For many remote sensing earth science applications, the most valuableinformation that may be derived from an image is contained in the edgessurrounding various objects of interest. Edge enhancement delineates theseedges and makes the shapes and details comprising the image more conspicuousand perhaps easier to analyze. Generally, what the eyes see as pictorial edgesare simply sharp changes in brightness value between two adjacent pixels. Theedges may be enhanced using either linear or nonlinear edge enhancementtechniques.Linear Edge Enhancement A straightforward method of extracting edges in remotely sensed imageryis the application of a directional first-difference algorithm and approximatesthe first derivative between two adjacent pixels. The algorithm produces thefirst difference of the image input in the horizontal, vertical, and diagonaldirections. The Laplacian operator generally highlights point, lines, and edges in theimage and suppresses uniform and smoothly varying regions. Human visionphysiological research suggests that we see objects in much the same way.Hence, the use of this operation has a more natural look than many of theother edge-enhanced images.Band ratioing Sometimes differences in brightness values from identical surface materialsare caused by topographic slope and aspect, shadows, or seasonal changes in
  • 90 Digital Image Processingsunlight illumination angle and intensity. These conditions may hamper theability of an interpreter or classification algorithm to identify correctly surfacematerials or land use in a remotely sensed image. Fortunately, ratiotransformations of the remotely sensed data can, in certain instances, be appliedto reduce the effects of such environmental conditions. In addition tominimizing the effects of environmental factors, ratios may also provide uniqueinformation not available in any single band that is useful for discriminatingbetween soils and vegetation. The mathematical expression of the ratio function is BVi,j,r = BVi,j,k/BVi,j.lwhere BVi,j,r is the output ratio value for the pixel at rwo, i, column j; BVi,j,kis the brightness value at the same location in band k, and BV i,j,l is thebrightness value in band l. Unfortunately, the computation is not alwayssimple since BV i,j = 0 is possible. However, there are alternatives. Forexample, the mathematical domain of the function is 1/255 to 255 (i.e., therange of the ratio function includes all values beginning at 1/255, passingthrough 0 and ending at 255). The way to overcome this problem is simplyto give any BVi,j with a value of 0 the value of 1. Ratio images can be meaningfully interpreted because they can be directlyrelated to the spectral properties of materials. Ratioing can be thought of asa method of enhancing minor differences between materials by defining theslope of spectral curve between two bands. We must understand that dissimilarmaterials having similar spectral slopes but different albedos, which are easilyseparable on a standard image, may become inseparable on ratio images. Figure5 shows a situation where Deciduous and Coniferous Vegetation crops outon both the sunlit and shadowed sides of a ridge. In the individual bands the reflectance values are lower in the shadowedarea and it would be difficult to match this outcrop with the sunlit outcrop.The ratio values, however, are nearly identical in the shadowed and sunlit areasand the sandstone outcrops would have similar signatures on ratio images.This removal of illumination differences also eliminates the dependence oftopography on ratio images.
  • Minakshi Kumar 91 Sunlight Figure 5: Reduction of Scene Illumination effect through spectral ratioing (source Lillesand & Kiefer, 1993) Landcover/ Illumination Digital Number Ratio Band A Band B Deciduous Sunlit 48 50 .96 Shadow 18 19 .95 Coniferous Sunlit 31 45 .69 Shadow 11 16 .69PRINCIPAL COMPONENT ANALYSIS The multispectral image data is usually strongly correlated from one bandto the other. The level of a given picture element on one band can to someextent be predicted from the level of that same pixel in another band. Principal component analysis is a pre-processing transformation that createsnew images from the uncorrelated values of different images. This isaccomplished by a linear transformation of variables that corresponds to arotation and translation of the original coordinate system. Principal component analysis operates on all bands together. Thus, italleviates the difficulty of selecting appropriate bands associated with the bandratioing operation. Principal components describe the data more efficiently
  • 92 Digital Image Processingthan the original band reflectance values. The first principal componentaccounts for a maximum portion of the variance in the data set, often as highas 98%. Subsequent principal components account for successively smallerportions of the remaining variance. Principal component transformations are used for spectral patternrecognition as well as image enhancement. When used before patternrecognition, the least important principal components are dropped altogether.This permits us to omit the insignificant portion of our data set and thusavoids the additional computer time. The transformation functions aredetermined during the training stage. Principal component images may beanalysed as separate black and white images, or any three component imagesmay be colour coded to form a colour composite. Principal componentenhancement techniques are particularly appropriate in areas where little apriori information concerning the region is available.IMAGE FUSION TECHNIQUES The satellites cover different portions of the electromagnetic spectrum andrecord the incoming radiations at different spatial, temporal, and spectralresolutions. Most of these sensors operate in two modes: multispectral modeand the panchromatic mode. The panchromatic mode corresponds to the observation over a broadspectral band (similar to a typical black and white photograph) and themultispectral (color) mode corresponds to the observation in a number ofrelatively narrower bands. For example in the IRS – 1D, LISS III operates inthe multispectral mode. It records energy in the green (0.52 – 0.59 µm), red(0.62-0.68 µm), near infrared (0.77- 0.86 µm) and mid-infrared (1.55 – 1.70µm). In the same satellite PAN operates in the panchromatic mode. SPOT isanother satellite, which has a combination of sensor operating in themultispectral and panchromatic mode. Above information is also expressedby saying that the multispectral mode has a better spectral resolution thanthe panchromatic mode. Now coming to the spatial resolution, most of the satellites are such thatthe panchromatic mode has a better spatial resolution than the multispectral mode,for e.g. in IRS -1C, PAN has a spatial resolution of 5.8 m whereas in the caseof LISS it is 23.5 m. Better is the spatial resolution, more detailed informationabout a landuse is present in the imagery, hence usually PAN data is used for
  • Minakshi Kumar 93observing and separating various feature. Both theses type of sensors have theirparticular utility as per the need of user. If the need of the user is to separatetwo different kind of landuses, LISS III is used, whereas for a detailed mappreparation of any area, PAN imagery is extremely useful. Image Fusion is the combination of two or more different images to forma new image (by using a certain algorithm). The commonly applied Image Fusion Techniques are 1. IHS Transformation 2. PCA 3. Brovey Transform 4. Band SubstitutionIMAGE CLASSIFICATION The overall objective of image classification is to automatically categorizeall pixels in an image into land cover classes or themes. Normally, multispectraldata are used to perform the classification, and the spectral pattern presentwithin the data for each pixel is used as numerical basis for categorization.That is, different feature types manifest different combination of DNs basedon their inherent spectral reflectance and emittance properties. The term classifier refers loosely to a computer program that implementsa specific procedure for image classification. Over the years scientists havedevised many classification strategies. From these alternatives the analyst mustselect the classifier that will best accomplish a specific task. At present it isnot possible to state that a given classifier is “best” for all situations becausecharacteristics of each image and the circumstances for each study vary sogreatly. Therefore, it is essential that the analyst understands the alternativestrategies for image classification. The traditional methods of classification mainly follow two approaches:unsupervised and supervised. The unsupervised approach attempts spectralgrouping that may have an unclear meaning from the user’s point of view.Having established these, the analyst then tries to associate an informationclass with each group. The unsupervised approach is often referred to as
  • 94 Digital Image Processingclustering and results in statistics that are for spectral, statistical clusters. Inthe supervised approach to classification, the image analyst supervises the pixelcategorization process by specifying to the computer algorithm; numericaldescriptors of the various land cover types present in the scene. To do this,representative sample sites of known cover types, called training areas ortraining sites, are used to compile a numerical interpretation key that describesthe spectral attributes for each feature type of interest. Each pixel in the dataset is then compared numerically to each category in the interpretation keyand labeled with the name of the category it looks most like. In the supervisedapproach the user defines useful information categories and then examines theirspectral separability whereas in the unsupervised approach he first determinesspectrally separable classes and then defines their informational utility. It has been found that in areas of complex terrain, the unsupervisedapproach is preferable to the supervised one. In such conditions if thesupervised approach is used, the user will have difficulty in selecting trainingsites because of the variability of spectral response within each class.Consequently, a prior ground data collection can be very time consuming.Also, the supervised approach is subjective in the sense that the analyst triesto classify information categories, which are often composed of several spectralclasses whereas spectrally distinguishable classes will be revealed by theunsupervised approach, and hence ground data collection requirements maybe reduced. Additionally, the unsupervised approach has the potentialadvantage of revealing discriminable classes unknown from previous work.However, when definition of representative training areas is possible andstatistical information classes show a close correspondence, the results ofsupervised classification will be superior to unsupervised classification.Unsupervised classification Unsupervised classifiers do not utilize training data as the basis forclassification. Rather, this family of classifiers involves algorithms that examinethe unknown pixels in an image and aggregate them into a number of classesbased on the natural groupings or clusters present in the image values. Itperforms very well in cases where the values within a given cover type are closetogether in the measurement space, data in different classes are comparativelywell separated. The classes that result from unsupervised classification are spectral classesbecause they are based solely on the natural groupings in the image values,
  • Minakshi Kumar 95the identity of the spectral classes will not be initially known. The analystmust compare the classified data with some form of reference data (such aslarger scale imagery or maps) to determine the identity and informational valueof the spectral classes. In the supervised approach we define useful informationcategories and then examine their spectral separability; in the unsupervisedapproach we determine spectrally separable classes and then define theirinformational utility. There are numerous clustering algorithms that can be used to determinethe natural spectral groupings present in data set. One common form ofclustering, called the “K-means” approach also called as ISODATA (InteractionSelf-Organizing Data Analysis Technique) accepts from the analyst the numberof clusters to be located in the data. The algorithm then arbitrarily “seeds”,or locates, that number of cluster centers in the multidimensional measurementspace. Each pixel in the image is then assigned to the cluster whose arbitrarymean vector is closest. After all pixels have been classified in this manner,revised mean vectors for each of the clusters are computed. The revised meansare then used as the basis of reclassification of the image data. The procedurecontinues until there is no significant change in the location of class meanvectors between successive iterations of the algorithm. Once this point isreached, the analyst determines the land cover identity of each spectral class.Because the K-means approach is iterative, it is computationally intensive.Therefore, it is often applied only to image sub-areas rather than to full scenes.Supervised classification Supervised classification can be defined normally as the process of samplesof known identity to classify pixels of unknown identity. Samples of knownidentity are those pixels located within training areas. Pixels located withinthese areas term the training samples used to guide the classification algorithmto assigning specific spectral values to appropriate informational class. The basic steps involved in a typical supervised classification procedureare illustrated on Fig. 6. The training stage Feature selection Selection of appropriate classification algorithm Post classification smoothening Accuracy assessment
  • 96 Digital Image Processing IMAGE DATA SET (Five digital numbers per pixel) CATEGORIZED SET (Digital numbers replaced by category types) Water Sand DN 1 Forest DN 2 DN 3 Urban DN 4Channel: 1 DN 5 2 Corn 3 4 Hay 5 (1) TRAINING STAGE (2) CLASSIFICATION (3) OUTPUT STAGE Collect numerical STAGES Present results; data from training Compare each unknown maps areas on speotral pixel to spectral patterns; tables of areas data response patterns assign to most similar GIS data files of land cover category categories Figure 6: Basic Steps in Supervised ClassificationTraining data Training fields are areas of known identity delineated on the digital image,usually by specifying the corner points of a rectangular or polygonal area usingline and column numbers within the coordinate system of the digital image.The analyst must, of course, know the correct class for each area. Usually theanalyst begins by assembling maps and aerial photographs of the area to beclassified. Specific training areas are identified for each informational categoryfollowing the guidelines outlined below. The objective is to identify a set ofpixels that accurately represents spectral variation present within eachinformation region (Fig. 7a).Select the Appropriate Classification Algorithm Various supervised classification algorithms may be used to assign anunknown pixel to one of a number of classes. The choice of a particular classifieror decision rule depends on the nature of the input data and the desiredoutput. Parametric classification algorithms assume that the observedmeasurement vectors Xc for each class in each spectral band during the trainingphase of the supervised classification are Gaussian in nature; that is, they arenormally distributed. Nonparametric classification algorithms make no suchassumption. Among the most frequently used classification algorithms arethe parallelepiped, minimum distance, and maximum likelihood decision rules.
  • Minakshi Kumar 97Parallelepiped Classification Algorithm This is a widely used decision rule based on simple Boolean “and/or” logic.Training data in n spectral bands are used in performing the classification.Brightness values from each pixel of the multispectral imagery are used toproduce an n-dimensional mean vector, Mc = (µck1, µc2, µc3, ... µcn) with µckbeing the mean value of the training data obtained for class c in band k outof m possible classes, as previously defined. Sck is the standard deviation ofthe training data class c of band k out of m possible classes. The decision boundaries form an n-dimensional parallelepiped in featurespace. If the pixel value lies above the lower threshold and below the highthreshold for all n bands evaluated, it is assigned to an unclassified category(Figs. 7c and 7d). Although it is only possible to analyze visually up to threedimensions, as described in the section on computer graphic feature analysis,it is possible to create an n-dimensional parallelepiped for classificationpurposes. The parallelepiped algorithm is a computationally efficient method ofclassifying remote sensor data. Unfortunately, because some parallelepipedsoverlap, it is possible that an unknown candidate pixel might satisfy the criteriaof more than one class. In such cases it is usually assigned to the first classfor which it meets all criteria. A more elegant solution is to take this pixelthat can be assigned to more than one class and use a minimum distance tomeans decision rule to assign it to just one class.Minimum Distance to Means Classification Algorithm This decision rule is computationally simple and commonly used. Whenused properly it can result in classification accuracy comparable to other morecomputationally intensive algorithms, such as the maximum likelihoodalgorithm. Like the parallelepiped algorithm, it requires that the user providethe mean vectors for each class in each hand µck from the training data. Toperform a minimum distance classification, a program must calculate thedistance to each mean vector, µck from each unknown pixel (BV ijk). It ispossible to calculate this distance using Euclidean distance based on thePythagorean theorem (Fig. 7b). The computation of the Euclidean distance from point to the mean ofClass-1 measured in band relies on the equation
  • 98 Digital Image Processing Dist = SQRT{ (BVijk - µck ) 2 + (BVijl - µcl) 2} Where µck and µcl represent the mean vectors for class c measured in bandsk and l. Many minimum-distance algorithms let the analyst specify a distance orthreshold from the class means beyond which a pixel will not be assigned toa category even though it is nearest to the mean of that category.Maximum Likelihood Classification Algorithm The maximum likelihood decision rule assigns each pixel having patternmeasurements or features X to the class c whose units are most probable orlikely to have given rise to feature vector x. It assumes that the training datastatistics for each class in each band are normally distributed, that is, Gaussian.In other words, training data with bi-or trimodal histograms in a single bandare not ideal. In such cases, the individual modes probably represent individualclasses that should be trained upon individually and labeled as separate classes.This would then produce unimodal, Gaussian training class statistics thatwould fulfil the normal distribution requirement. The Bayes’s decision rule is identical to the maximum likelihood decisionrule that it does not assume that each class has equal probabilities. A prioriprobabilities have been used successfully as a way of incorporating the effectsof relief and other terrain characteristics in improving classification accuracy.The maximum likelihood and Bayes’s classification require many morecomputations per pixel than either the parallelepiped or minimum-distanceclassification algorithms. They do not always produce superior results.Classification Accuracy Assessment Quantitatively assessing classification accuracy requires the collection ofsome in situ data or a priori knowledge about some parts of the terrain whichcan then be compared with the remote sensing derived classification map. Thusto assess classification accuracy it is necessary to compare two classificationmaps 1) the remote sensing derived map, and 2) assumed true map (in factit may contain some error). The assumed true map may be derived from insitu investigation or quite often from the interpretation of remotely senseddata obtained at a larger scale or higher resolution.
  • Minakshi Kumar 99Band 3 digital number Band 3 digital number Figure 7a: Pixel observations from selected Figure 7b: Minimum Distance to Means training sites plotted on scatter diagram Classification strategyBand 3 digital number Figure 7d: Stepped parallelepipeds to avoid overlap (source Lillesand and Figure 7c: Parallelepiped classification strategy Kiefer, 1993) Classification Error Matrix One of the most common means of expressing classification accuracy is the preparation of classification error matrix sometimes called confusion or a contingency table. Error matrices compare on a category by category basis, the relationship between known reference data (ground truth) and the corresponding results of an automated classification. Such matrices are square, with the number of rows and columns equal to the number of categories whose classification accuracy is being assessed. Table 1 is an error matrix that an image analyst has prepared to determine how well a Classification has categorized a representative subset of pixels used in the training process of a supervised classification. This matrix stems from classifying the sampled
  • 100 Digital Image Processingtraining set pixels and listing the known cover types used for training (columns)versus the Pixels actually classified into each land cover category by theclassifier (rows).Table 1. Error Matrix resulting from classifying training Set pixels W S F U C H Row Total W 480 0 5 0 0 0 485 S 0 52 0 20 0 0 72 F 0 0 313 40 0 0 353 U 0 16 0 126 0 0 142 C 0 0 0 38 342 79 459 H 0 0 38 24 60 359 481 Column 480 68 356 248 402 438 1992 TotalClassification data Training set data ( Known cover types)Producer’s Accuracy Users AccuracyW= 480/480 = 100% W= 480/485 = 99%S = 052/068 = 16% S = 052/072 = 72%F = 313/356 = 88% F = 313/352 = 87%U =126/241l = 51% U = 126/147 = 99%C = 342/402 = 85% C = 342/459 = 74%H = 359/438 = 82% H = 359/481 = 75%Overall accuracy = (480 + 52 + 313+ 126+ 342 +359)/1992= 84%W, water; S, sand; F, forest; U, urban; C, corn; H, hay(source Lillesand and Kiefer, 1993). An error matrix expresses several characteristics about classificationperformance. For example, one can study the various classification errors of
  • Minakshi Kumar 101omission (exclusion) and commission (inclusion). Note in Table 1 the trainingset pixels that are classified into the proper land cover categories are locatedalong the major diagonal of the error matrix (running from upper left to lowerright). All non-diagonal elements of the matrix represent errors of omissionor commission. Omission errors correspond to non-diagonal column elements(e.g. 16 pixels that should have classified as “sand” were omitted from thatcategory). Commission errors are represented by non-diagonal row elements(e.g. 38 urban pixels plus 79 hay pixels were improperly included in the corncategory). Several other measures for e.g. the overall accuracy of classification can becomputed from the error matrix. It is determined by dividing the total numbercorrectly classified pixels (sum of elements along the major diagonal) by thetotal number of reference pixels. Likewise, the accuracies of individual categoriescan be calculated by dividing the number of correctly classified pixels in eachcategory by either the total number of pixels in the corresponding rows orcolumn. Producers accuracy which indicates how well the training sets pixelsof a given cover type are classified can be determined by dividing the numberof correctly classified pixels in each category by number of training sets usedfor that category (column total). Users accuracy is computed by dividing thenumber of correctly classified pixels in each category by the total number ofpixels that were classified in that category (row total). This figure is a measureof commission error and indicates the probability that a pixel classified into agiven category actually represents that category on ground. Note that the error matrix in the table indicates an overall accuracy of84%. However producers accuracy ranges from just 51% (urban) to 100%(water) and users accuracy ranges from 72% (sand) to 99% (water). This errormatrix is based on training data. If the results are good it indicates that thetraining samples are spectrally separable and the classification works well inthe training areas. This aids in the training set refinement process, but indicateslittle about classifier performance else where in the scene.Kappa coefficient Kappa analysis is a discrete multivariate technique for accuracy assessment.Kappa analysis yields a Khat statistic that is the measure of agreement ofaccuracy. The Khat statistic is computed as
  • 102 Digital Image Processing N ∑ x ii (∑ x i + *x + i ) r Khat = 2 N − ∑ (x i + + *x +i ) r rWhere r is the number of rows in the matrix xii is the number of observationsin row i and column i, and xi+ and x+i are the marginal totals for the row iand column i respectively and N is the total number of observations.CONCLUSIONS Digital image processings of satellite data can be primarily grouped intothree categories : Image Rectification and Restoration, Enhancement andInformation extraction. Image rectification is the pre-processing of satellite datafor geometric and radiometric connections. Enhancement is applied to imagedata in order to effectively display data for subsequent visual interpretation.Information extraction is based on digital classification and is used forgenerating digital thematic map.REFERENCESCampbell, J.B. 1996. Introduction to Remote Sensing. Taylor & Francis, London.ERDAS IMAGINE 8.4 Field Guide: ERDAS Inc.Jensen, J.R. 1996. Introduction to Digital Image Processing : A Remote Sensing Perspective. Practice Hall, New Jersey.Lillesand, T.M. and Kiefer, R. 1993. Remote Sensing Image Interpretation. John Wiley, New York.